Study on Structural, Electronic, Optical and Mechanical ...article.ajmp.org/pdf/10.11648.j.ajmp.20150402.15.pdf · Md. Atikur Rahman *, Md. Zahidur Rahaman Department of Physics,

American Journal of Modern Physics 2015; 4(2): 75-91

Published online April 8, 2015 (http://www.sciencepublishinggroup.com/j/ajmp)

doi: 10.11648/j.ajmp.20150402.15

ISSN: 2326-8867 (Print); ISSN: 2326-8891 (Online)

Study on Structural, Electronic, Optical and Mechanical Properties of MAX Phase Compounds and Applications Review Article

Md. Atikur Rahman*, Md. Zahidur Rahaman

Department of Physics, Pabna University of Science and Technology, Pabna-6600, Bangladesh

Email address: [email protected] (Md. Atikur Rahman)

To cite this article: Md. Atikur Rahman, Md. Zahidur Rahaman. Study on Structural, Electronic, Optical and Mechanical Properties of MAX Phase Compounds

and Applications Review Article. American Journal of Modern Physics. Vol. 4, No. 2, 2015, pp. 75-91. doi: 10.11648/j.ajmp.20150402.15

Abstract: The term “MAX phase” refers to a very interesting and important class of layered ternary transition-metal

carbides and nitrides with a novel combination of both metal and ceramic-like properties that have made these materials highly

regarded candidates for numerous technological and engineering applications. A relatively new class of transition metal layered

compounds Mn+1AXn, (MAX phases) where M is an early transition metal, A is a group A element most likely Al, and X is C or

N with n = 1, 2, 3………..Due to their unique structural arrangements and directional bonding, these ternary compounds

possess some very outstanding mechanical and chemical properties such as damage-resistance, oxidation resistance, excellent

thermal and electric conductivity, machinability, and fully reversible dislocation-based deformation. These properties can be

explored in the search for new phases and their composites to meet the performance goals of advanced materials with

applications in fossil energy conversion technology. Systematic and detailed computational studies on MAX phase compounds

can provide fundamental understanding of the key characteristics that lead to these desirable properties and to the discovery of

other new and better alloys.In this paper, we review on structural, electronic, optical and mechanical properties of around 50

MAX phase compounds and their applications. From the comparative study on the result of these compounds we think that this

paper will enable to researcher to explore and predict new MAX phases and new composite alloys with better physical

properties as advanced materials for various applications at extreme conditions.

Keywords: MAX Phase Compounds, Electronic, Optical and Mechanical Properties, Applications

1. Introduction

Metallic materials are typically characterized by being

thermally and electrically conductive, plastically deformable

at room temperature, readily machinable, thermal shock

resistant, damage tolerant, relatively soft, etc. On the other

hand, ceramics are generally characterized by high elastic

moduli, good high temperature mechanical properties, good

oxidation and corrosion resistance, etc. The relatively recent

discovery of a family of new materials, namely the MAX

phases [1] (also termed in some publications ‘metallic

ceramics’ [2]) has provided materials that possess a useful

combination of both metallic and ceramic characteristics.

Recently, the interest in nanolaminated ternary Mn+1AXn

(denoted 211, 312 and 413, where n=1, 2 and 3, respectively)

carbides and nitrides, so-called MAX-phases, has grown

significantly. МАХ phases are a family of ternary layered

compounds with the formal stoichiometry Mn+1AXn (n = 1, 2,

3. …), where М is the transition d metal; А is the p element

(e.g., Si, Ge, Al, S, Sn, etc.); X is carbon or nitrogen. Most of

the MAX phases are 211 phases, some are 312s, and the rest

are 413s.The M group elements include Ti, V, Cr, Zr, Nb, Mo,

Hf, and Ta. The A elements include Al, Si, P, S, Ga, Ge, As,

Cd, In, Sn, Tl, and Pb. The X elements are either C and/or N.

First reports on the synthesis of МАХ phases were presented

in the works by Novotnoi et al. [3-7] performed in the 60’s of

the last century. Intensive studies of the physicochemical

properties of МАХ phases, started in the middle of the

1990’s, led to the conclusion that they were a unique class of

layered materials combining chemical, physical, electrical,

and mechanical properties inherent to both metals and

ceramics [8]. Thus, similarly to metals, МАХ phases have

good heat and electric conductivity and at the same time, like

ceramics, they are refractory, oxidation and corrosion

resistant and have low density. These properties can be

explored in the search for new phases and their composites

American Journal of Modern Physics2015; 4(2): 75-91 76

that have potential to meet the performance goals for

materials to be used in the next generation of fossil energy

power systems at a significantly reduced cost. МАХ phases

are at present of increased interest as promising materials for

polyfunctional high-temperature ceramics, protective

coatings, sensors, and electrical contacts for catalysis. The

current stage of the experimental studies of МАХ phases is

marked by the development of synthesis methods for these

compounds, including in film and nanocrystalline states, and

also by the discovery of new phases [9-11]. For example, by

the magnetron deposition method new phases of Ti4SiC3 and

Ti4GeC3 (in the film state) along with a few others [11] have

fairly recently been synthesized [12, 13]. Note that at present

the family consists of 60 compounds [11] involving many d

and p elements as components (Fig. 1). Moreover, detailed

investigations of the functional properties of МАХ phases (in

particular, doping and non-stoichiometry effects,

polymorphism, tribological, mechanical, and newly found

[14, 15] superconducting properties, etc.) as well as further

searches for the promising technological use of these

materials are being conducted [11].

Fig. 1. Periodic table of elements forming nanolaminates of the general composition Mn+1AXn (n= 1, 2, 3 ….), where M is a transition d metal, A is a pelement

(Si, Al, S, Sn, etc), and X is carbon or nitrogen.

There are more than 70 known phases of MAX

compounds and this number is rapidly growing. A list of

MAX phase compounds are shown in Table 1.

Table 1. A list of the MAX phases known to date, in both bulk and thin film form.

211 Phases 312 Phases 413 Phases Ti2CdC, Sc2InC, Ti2AlC, Ti2GaC, Ti2InC, Ti2TlC, V2AlC, Ti3AlC2, Ti4AlN3,

Cr2GaC, Ti2AlN, Ti2GaN, Ti2InN, V2GaC, V2GaN, Cr2GaN, V3AlC2, V4AlC3,

Ti2PbC, V2GeC, Cr2AlC, Cr2GeC, Ti2GeC, Ti2SnC, V2PC, Ti3SiC2, Ti4GaC3,

Zr2TlC, Nb2AlC, Nb2GaC, Nb2InC, V2AsC, Ti2SC, Zr2InC, Ti3GeC2, Ti4SiC3,

Zr2PbC, Nb2SnC, Nb2PC,Mo2GaC, Zr2InN, Zr2TlN, Zr2SnC, Ti3SnC2, Ti4GeC3,

Nb2AsC, Zr2SC, Nb2SC, Hf2InC, Hf2TlC, Ta2AlC, Ta2GaC, Ta3AlC2 Nb4AlC3,

Hf2SnC, Hf2PbC, Hf2SnN, Hf2SC Ta4AlC3

Fig. 2. Crystal structure of 211, 312, 413, 514 phases of M=Ta, A=Al and X=C.

In this article, we review the electronic structure and mechanical properties of MAX phase compounds which have

77 Md. Atikur Rahman and Md. Zahidur Rahaman: Study on Structural, Electronic, Optical and Mechanical Properties of

MAX Phase Compounds and Applications Review Article

been done using first-principles methods. Some of them are:

Ti3AC2 (A = Al, Si, Ge), Ti2AC (A = Al, Ga, In, Si, Ge, Sn, P,

As, S), Ti2AlN, M2AlC (M = V, Nb, Cr), Tan+1AlCn (n = 1 to

4), Hf2TlC, Hf2SnC, Hf2PbC, Hf2SnN and Hf2SC (see Table

1).Most of them are Ti-containing phases, since they are the

most common in MAX phases. They are chosen for a wide

representation and for studying specific trends. The first 12

vary only by the A element and involve three (3 1 2) phases

and the nine (2 1 1) phases. In addition to carbides, one

example of nitride, Ti2AlN is also included. This is followed

by three other (2 1 1) phases, (V, Nb, Cr)2AlC where the

transition metal M have different d-electron configurations.

The Ta-Al-C group is chosen to study the effect of the

number of MX layers (see Fig.2). The calculated results

include: band structures, total and partial density of states,

effective atomic charges, quantitative bond order values,

interband optical conductivities, elastic coefficients, bulk

modulus, shear modulus, Young’s modulus, and Poisson’s

ratio. By systematically analyzing these results and in

comparison with available experimental data, several

important features on structural stability, interatomic bonding

and optical conductivities are identified. These results enable

us to build a data base to facilitate the search for new MAX

phases and new composite alloys with the potential of having

better physical properties as advanced materials.

The publication of papers on the MAX phases has shown

an almost exponential increase in the past decade. The

existence of further MAX phases has been reported or

proposed. In addition to surveying this activity, the synthesis

of MAX phases in the forms of bulk, films and powders is

reviewed, together with their physical, mechanical and

corrosion/oxidation properties. Recent research and

development has revealed potential for the practical

application of the MAX phases (particularly using the

pressureless sintering and physical vapour deposition coating

routes) as well as of MAX based composites. The challenges

for the immediate future are to explore further and

characterize the MAX phases reported to date and to make

further progress in facilitating their industrial application.

2. Early History of MAX Phase Compounds

The MAX phases have two histories. The first spans the

time they were discovered in the early and mid-1960s to

roughly the mid-1990s, when, for the most part, they were

ignored. The second is that of the last 15 years or so, when

interest in these phases has exploded. The ternary compound,

Ti3SiC2, was first synthesized and fully characterized by Dr.

Michel Barsoum's research group at Drexel University in the

1990s. A year later they showed that this compound was but

one of over sixty phases,[16] most discovered and produced

in powder form in the 1960s by H. Nowotny and coworkers

[17]. In 1999 they discovered Ti4AlN3 and realized that they

were dealing with a much larger family of solids that all

behaved similarly. Since 1996, when the first paper was

published on the subject, tremendous progress has been made

in understanding the properties of these phases and the 1996

article [18] has been cited over 650 times [19].

3. Crystal Structures of MAX Phase Compounds

Fig. 2.1. Unit cells of (a) 211, (b) 312 and (c) 413 phases. The c parameters

are depicted by vertical dashed lines. dx denotes the thickness- from atom

center to center of the Mn+1Xn layers; dα that of A layers. It follows that that

for the 211 phases c= 2 dα + 2 dx. Also shown are the various z values (see

Table 2).

Fig. 3. Schematics of (1120) planes in (a) M2AX, (b) α-M3AX2, (c) β-M3AX2,

(d) α-M4AX3, (e) β-M4AX3 and (f) γ- M4AX3. Note that it is only in the α-

M3AX2 structure that the A atoms lie on top of each other.

MAX-phase crystals have a hexagonal symmetry in space

group P63/mmc. For the 211 structure, there are three

inequivalent atoms; in the 312, there are four, and in the 413,

there are five. The coordinates and internal parameters ZM of

all the atoms are listed in Table 2 for the various polymorphs.

For the 211 phases, there is only one polymorph (Figure 3a).

In the 312 case there are two, α and β, shown in Figures 3b

and c, respectively. For the 413 phases, there are three


polymorphs, viz. α, β, and γ, shown in Figures 3d, e and f,

respectively. The density (D) and lattice parameters (a, c) of

MAX phase compounds are listed in Table 3 [22-35].

Table 2. Sites and idealized coordinates of the Mn+1AXn phases for n = 1-3. Also listed are the currently known polymorphs. The fifth column lists the canonical

positions.

Atoms Chemistry/archetypical phase ZM Range Notes and reference

M2AX / Ti2SC - Kudielka and Rohde (1960)

Wyckoff x y Zi (canonical) - -

A 2d 1/3 2/3 ¾ -

M 4f 2/3 1/3 1/12 (0.083) 0.07-0.1 ZM in Figure 2.1a

X 2a 0 0 0 -

α-M3AX2/Ti3SiC2 Jeitschko and Nowotny (1967)

A 2b 0 0 4/16 - -

Ml 4f 1/3 2/3 2/16 (0.125) 0.131- 0.138 ZM1 in Figure 2.1b

MII 2a 0 0 0 - -

X l 4f 2/3 1/3 1/16 (0.0625) 0.0722 ZC in Figure 2.1b

β-M3AX2/Ti3SiC2 Farber et al. (1999)

A 2d 1/3 2/3 4/16 - Should be quite similar in

Ml 4f 1/3 2.3 2/16 (0.125) 0.1355 Properties to α-M3AX2

MII 2a 0 0 0 -

X l 4f 2/3 1/3 1/16 (0.0625) 0.072

α-M4AX3/Ti4AlN3 Barsoum et al. (1999c) and Rawn et al. (2000)

A 2c 1/3 2/3 5/20 - -

Ml 4e 0 0 3/20 (0.15) 0.155-0.158 ZM1 in Figure 2.1c

MII 4f 1/3 2/3 1/20 (0.05) 0.052-0.055 ZM2 in Figure 2.1c

X l 2a 0 0 0 - -

XII 4f 2/3 1/3 2/20 0.103-0.109 ZC in Figure 2.1c

β-M4AX3/Ta4AlC3 Eklund et al. (2007)

A 2c 1/3 2/3 5/20 - -

Ml 4e 1/3 2/3 12/20 (0.6) 0.658 -

MII 4f 1/3 2/3 1/20 0.055 Eklund et al. (2007)

X l 2a 0 0 0 - -

XII 4e 2/3 1/3 2/20 0.103 -

γ-M4AX3/Ta4GaC3 Etzkorn et al. (2009)

A 2c 1/3 2/3 5/20 - -

Ml 4e 0 0 3/20 (0.15) 0.156 -

MII 4f 1/3 2/3 1/20 0.056 Etzkorn et al. (2009) and He et al. (2011)

X l 2a 0 0 0 - -

XII 4f 2/3 1/3 2/20 0.1065 -

Table 3. Density and lattice parameters of 77 Max phase compounds.

No. Compounds Density D, ( Mgm-3) Lattice parameters a, c(Å)

211 Phases

1 Sc2AlC 2.99 3.280, 15.373

2 Sc2GaC 3.93 3.253, 15.813

3 Sc2InC 4.72 3.272, 16.452

4 Sc2TlC 6.60 3.281, 16.530

5 Ti2AlC 4.11 3.051, 13.637

6 Ti2AlN 4.31 2.989, 13.614

7 Ti2SiC 4.35 3.052, 12.873

8 Ti2PC 4.56 3.191, 11.457

9 Ti2SC 4.62 3.216, 11.22

10 Ti2GaC 5.53 3.07, 13.52

11 Ti2GaN 5.75 3.00, 13.3

12 Ti2GeC 5.30 3.07, 12.93

13 Ti2AsC 5.71 3.209, 11.925

14 Ti2CdC 9.71 3.1, 14.41

15 Ti2InC 6.30 3.134, 14.077

16 Ti2InN 6.54 3.07, 13.97

17 Ti2SnC 6.10 3.163, 13.679

18 Ti2TlC 8.63 3.15, 13.98

19 Ti2PbC 8.55 3.20, 13.81



No. Compounds Density D, ( Mgm-3) Lattice parameters a, c(Å)

20 V2AlC 4.07 3.1, 13.83

21 V2SiC 5.20 2.955, 11.983

22 V2PC 5.38 3.077, 10.91

23 V2GaC 6.39 2.93, 12.84

24 V2GaN 5.94 3.00, 13.3

25 V2GeC 6.49 3.00, 12.25

26 V2AsC 6.63 3.11, 11.3

27 Cr2AlC 5.21 2.863, 12.814

28 Cr2GaC 6.81 2.88, 12.61

29 Cr2GaN 6.82 2.875, 12.77

30 Cr2GeC 6.88 2.95, 12.08

31 Zr2AlC 5.78 3.2104, 14.2460

32 Zr2AlN 5.83 3.2155, 14.2134

33 Zr2SC 6.20 3.40, 12.13

34 Zr2InC 7.1 3.34, 14.91

35 Zr2InN 7.53 3.27, 14.83

36 Zr2SnC 6.9 3.3576, 14.57

37 Zr2TlC 9.17 3.36, 14.78

38 Zr2TlN 9.60 3.3, 14.71

39 Zr2PbC 8.2 3.38, 14.66

40 Nb2AlC 6.50 3.10, 13.8

41 Nb2PC 7.09 3.28, 11.5

42 Nb2SC0.4 7.01 3.27, 11.4

43 Nb2SCx - -

44 Nb2GaC 7.73 3.13, 13.56

45 Nb2InC 8.3 3.17, 14.37

46 Nb2SnC 8.3 3.214, 13.802

47 Nb2AsC 8.025 3.31, 11.9

48 Mo2GaC 8.79 3.01, 13.18

49 Hf2AlC 10.23 3.2121, 14.3830

50 Hf2AlN 10.92 3.1380, 14.1872

51 Hf2SC 11.36 3.36, 11.99

52 Hf2InC 11.24 3.309, 14.723

53 Hf2SnC 11.2 3.320, 14.388

54 Hf2SnN 7.72 3.31, 14.3

55 Hf2TlC 13.65 3.32, 14.62

56 Hf2PbC 11.5 3.55, 14.46

57 Ta2AlC 11.46 3.079, 13.860

58 Ta2GaC 13.05 3.10, 13.57

312 Phases

1 Ti3SiC2 4.52 3.0665, 17.671

2 Ti3AlC2 4.2 3.065, 18.487

3 Ti3GeC2 5.22 3.07, 17.76

4 Ti3SnC2 5.99 3.1366, 18.650

5 V3SiC2 5.27 2.915, 17.535

6 (V0.5Cr0.05)3AlC2 5.31 2.892, 17.73

7 Nb3SiC2 7.22 3.13, 17.94

8 Ta3AlC2 12.43 3.0930, 19.159

413 Phases

1 Ti4AlN3 4.58 2.988, 23.372

2 Ti4SiC3 4.65 3.05, 22.67

3 Ti4GeC3 - -, 22.7

4 V4AlC3 5.24 2.931, 22.719

5 Nb4AlC3 6.97 3.123, 24.109

6 α-Nb4SiC3 - 3.1819, 22.9877

7 Ta4AlC3 13.18 3.092, 23.708

8 Ti4GaC3 5.17 3.0690, 23.440

514 Phase

1 Ti5SiC4 4.81 3.04, 27.24

615 Phase

1 Ta6AlC5 13.69 3.078, 34.681

716 Phase

1 Ti7SnC6 4.80 3.2, 4.1


Fig. 4. Calculated DOS and atom-resolved PDOS of 20 MAX phase compounds.



Fig. 5. Optical conductivities of 20 MAX phase compounds. Blue (red) curve show the planer (axial direction).

4. Comparative Study on Electronic, Optical and Mechanical Properties of MAX Phase Compounds

4.1. Electronic and Optical Properties

The electronic structure and optical conductivities of the

MAX phases were calculated using the first-principles

orthogonalized linear combination of atomic orbitals

(OLCAO) method which is based on the local density

approximation (LDA) of density functional theory [58-59].

This method has been demonstrated to be highly accurate

and efficient when dealing with materials with complex

structures for both crystalline [60-66] and non-crystalline

systems [67-71]. Details of the electronic structure and

optical conductivity of 20 MAX phase compounds were

reported using OLCAO in reference [20].In this review

article we studied only some selected results. Fig. 4 shows

the total density of states (TDOS) and atom-resolved partial

density of states (PDOS) of the 20 MAX phases compounds.

The local feature of the total density of states (TDOS) curve

around the Fermi-level (Ef) is a reasonable indicator of the

intrinsic stability of a crystal. A local minimum at Ef implies

higher structural stability because it signifies a barrier for

electrons below the Ef(E< 0 eV) to move into unoccupied

empty states (E> 0 eV); whereas a local maximum at Ef is

usually a sign of structural instability. This semi-

quantitative criterion works reasonably well for the results

of Fig.1. Ti2InC, Ti2SC, and Cr2AlC have a local minimum

at Ef, suggesting a higher level of stability. Ti2PC, Ti2AsC,

and Ta5AlC4 show a peak in the TDOS at Ef. These facts

correlate quite well with the observation that the first group

of MAX phases are easier to synthesize whereas those in

the second group are not [20]. The calculated optical

conductivities in the 20 MAX phase compounds for

frequency range between 0 and 10 eV are shown in Fig. 5.

The spectra are resolved into two components, one is the

planar (a-b plane) component and the other is the axial (c-

direction) component, or σ1, planar and σ1, axial for short. The

number indicated in each plot is the anisotropy ratio, or the

averaged (σ1, planar/σ1,axial) ratio over all the data points.


From these plots, several interesting observations can be

made [20]. Most of the MAX phases have the maximum

optical conductivities around 5 eV and several phases show

sharp peak structures with considerable anisotropy

especially in the Ta series. The optical conductivity may be

related to the electric conductivity in MAX phases if intra-

band contribution at the frequency near 0.0 eV can be

accounted for. It is conceivable that the anisotropy in

optical conductivity in the low energy range could also

imply that there may be similar trends in the electrical

conductivity. The optical anisotropy in the low energy range

of the calculation is quite low for the majority of the 20

phases which correlates well with the low anisotropy in the

measured electrical conductivities. A notable exception is

Nb2AlC. Indeed, experiments by T. H. Scabarozi et al. [21]

showed that Nb2AlC has a significantly larger anisotropy in

its electrical conductivity than other MAX-phase

compounds.

4.2. Mechanical and Elastic Properties

Elastic constants are very important material parameters.

Evident and direct application of elastic constants is in the

evaluation of elastic strains or energies in materials under

stresses of various origins: external, internal and thermal

[75]. The elastic constants can also provide information on

the stability, stiffness, brittleness, ductility, and anisotropy

of a material and propagation of elastic waves and normal

mode oscillations. Moreover, knowledge of the values of

elastic constants is crucial for a sound understanding of the

mechanical properties of the relevant material. The most

important parameters for estimating mechanical properties

of materials are bulk modulus (B), shear modulus (G),

Young’s modulus (E) and Poisson’s ratio (ν). In this section

we have studied about these properties. Elastic deformation

in crystalline solids is a fully reversible and nondissipative

process. For hexagonal symmetry, there are five

independent elastic constants; they are C11, C12, C13, C33,

and C44. To date, the nonavailability of large MAX single

crystals has made it difficult to experimentally determine

their elastic constants. What can be used until such

measurements are available, however, are the results of ab

initio calculations. In this article all the mechanical

properties and elastic constant of MAX phases compounds

are summarized and reviewed. All the properties are

calculated by using density functional theory (DFT). The

bulk moduli Bv and Young’s moduli Ev are calculated by

using equations 1 and 2. Also the shear moduli Gv and

Poisson’s ratio ν are calculated by using equations 3 &

4.The calculated results for these moduli are listed in table

4.

�� = �

�(� + �� + 2�� +

��

�) (1)

�� = ��

�� (2)

�� =

�(2� + �� − �� − 2��) +

� [2�� +

�(� − ��)] (3)

� = ��

� (�� ) (4)

The Poisson’s ratio (S) defined as the ratio of transverse

strain to the longitudinal strain is used to reflect the stability

of the material against shear and provides information about

the nature of the bonding forces. It takes value: -1 <ν <1/2.

No real material is known to have a negative value of ν. So

this inequality can be replaced with 0 < ν < 1/2. Bigger the

Poisson’s ratio betters the plasticity. The calculated result of

the Poisson’s ratio shown in table 4 indicates that the max

phase compound is of good plasticity. The ν = 0.25 and ν =

0.5 are the lower limit and upper limit for central forces in

solids, respectively. The obtained value of Poisson’s ratio of

Ta2GaN, Cr2GeC and α-Ta4AlC3 are larger than the lower

limit value, which indicates that the interatomic forces of

those compounds are central forces. The bulk modulus is

usually assumed to be a measure of resist deformation

capacity upon applied pressure [76]. The larger the value of

bulk modulus is, the stronger capacity of the resist

deformation is. From figure 6 we can make a clear idea

about the ability to resist deformation of Max phases.

Similarly, the shear moduli are a measure of resist

reversible deformation by shear stress [76]. The larger the

value is, the stronger capacity of the resist shear

deformation is. From Figure 6 we can make a clear idea

about this. Furthermore, Young’s modulus is defined as the

ratio between stress and strain, and it also provided a

measure of stiffness of the solid materials. The larger the

value is, the stiffer the material is. The calculated result

shows that the stiffness of β -Ta4AlC3 is the largest among

all Max phases which we studied.

The elastic parameters as presented in Tables 4 allow us

to make the following conclusions.

(i) The Cij constants for all MAX phases are positive and

satisfy the generalized criteria in Ref. [72] for mechanically

stable crystals: C44>0, C11>|C12|, and (C11+C12) C33>2C213.

(ii) Among the MAX phases, α-Ta4AlC3 is the phase with

the largest bulk modulus (~266 GPa), while Ti2CdC has the

smallest Bv ~115.66 GPa. We have also seen that β -Ta4AlC3

has maximum Young’s modulus (~404) GPa whereTi2CdC

and Zr2PbC have the smallest Ev ~174 GPa.

(iii) The Young’s modulus is defined as the ratio between

stress and strain and is used to provide a measure of

stiffness, i.e., the larger the value of Ev, the stiffer the

material. In our case β -Ta4AlC3> α-V4AlC3> V2PC > α-

Ta4AlC3> Ti4AlN3> α-Nb4AlC3> Cr2AlC > Ti3GeC2>

Ti4GeC3> Hf2SC > Nb2PC > Ta4GaC3> V2GaC >

V2AlC …………….. Hf2PbC > Ti2PbC > Zr2PbC (see

details in Table 5).The maximum and minimum shear

moduli are obtained in Ti4AlN3 and Zr2PbC. The ascending

to descending values of bulk modulus (Bv), Young’s

modulus (Ev), shear modulus (Gv) and Possion’s ratio of all

the MAX phases compounds are shown in details in Table 5.

(iv) Poisson’s ratios for most of the MAX phases are

around 0.2 (Table 4), which is lower than the 0.3 of Ti and

most metals, and closer to the 0.19 of near-stoichiometric

TiC. According to Pugh’s criteria [73], a material should

behave in a ductile manner if G/B<0.5, otherwise it should

be brittle. In our case, all the compounds have G/B< 0.5,

(Table 5) therefore all the MAX phases compounds show

ductile behavior.



Table 4. Summary of 50 MAX phase compounds, elastic constants Cij determined from ab-initio calculations. Also the values of Bv, Ev, Gv, and ν are listed

calculated using Equations 1, 2, 3 & 4 respectively.

Compounds C11 C12 C13 C33 C44 Bv Ev Gv ν Ref.

413 Phases

Ti4AlN3 420 73 70 380 128 182.88 359 153 0.172 36

Ti4GeC3 381 96 95 349 148 187.00 341 143 0.195 37

α-Ta4AlC3 437 158 197 416 165 266.00 364 143 0.272 38

β -Ta4AlC3 509 143 156 440 147 263.11 404 162 0.244 39

Ta4GaC3 389 84 78 323 131 175.66 332 140 0.185 40

α-V4AlC3 435 121 105 384 168 212.88 384 160 0.199 39

α-Nb4AlC3 413 124 135 328 161 215.77 353 144 0.227 39

312 Phases

Ti3SiC2 365 125 120 375 122 203.88 307 123 0.248 42

Ti3GeC2 355 143 80 404 172 191.11 345 144 0.198 43

Ti3AlC2 361 75 70 299 124 161.22 321 132 0.178 44

Ti3SnC2 346 92 84 313 123 169.44 300 124 0.205 41

211 Phases

Ti2AlN 342 56 96 283 123 162.55 300 126 0.192 36

Ti2AlC 301 59 55 278 113 135.33 272 117 0.164 45

Ti2SnC 260 78 70 254 93 134.44 226 93 0.218 54

Ti2GeC 279 99 95 283 125 157.66 257 105 0.227 48

Ti2GaC 314 66 59 272 122 140.88 283 121 0.166 49

Ti2SC 315 98 99 362 161 176.00 310 127 0.209 46

Ti2CdC 258 68 46 205 33 115.66 174 69.6 0.249 53

Ti2InC 288 62 53 248 88 128.88 241 102 0.186 53

Ti2InN 229 56 106 248 92 138.00 208 83.3 0.248 54

Ti2PbC 235 90 53 211 66 119.22 182 73.2 0.245 54

V2AlC 346 71 106 314 151 174.66 324 136 0.190 51

V2GeC 282 121 95 259 160 160.55 277 114 0.212 47

V2GaC 343 67 124 312 157 180.88 326 136 0.199 49

V2GaN 281 71 142 293 128 173.88 263 106 0.246 54

V2AsC 334 109 157 321 170 203.88 318 128 0.240 57

V2PC 376 113 168 386 204 226.22 376 154 0.222 54

Cr2AlC 384 79 107 382 147 192.88 351 146 0.197 52

Cr2GeC 315 99 146 354 89 196.22 249 96.7 0.288 47

Cr2GaC 312 81 139 325 128 185.22 283 114 0.244 54

Mo2GaC 294 98 107 289 127 166.77 257 111 0.227 54

Nb2AlC 310 90 118 289 139 173.44 285 116 0.226 54

Nb2GaC 309 80 138 262 126 176.88 270 108 0.246 54

Nb2SnC 341 106 169 321 183 210.11 314 134 0.237 56

Nb2InC 291 76 108 267 102 159.22 247 99.4 0.241 54

Nb2AsC 334 104 169 331 167 209.22 317 127 0.247 57

Nb2PC 369 113 171 316 170 218.22 333 134 0.245 54

Hf2SC 344 116 138 369 175 204.55 336 137 0.226 50

Hf2SnC 318 96 99 301 123 169.44 280 114 0.225 55

Hf2SnN 240 62 103 236 92 139.11 211 84.5 0.247 54

Hf2InC 284 69 65 243 91 134.33 238 98.7 0.204 57

Hf2PbC 241 77 70 222 69 126.44 191 81 0.236 54

Ta2AlC 334 114 130 322 148 193.11 303 122 0.239 54

Ta2GaC 335 106 137 315 137 193.88 294 118 0.247 54

Ta2GaN 333 187 150 364 141 222.66 277 107 0.292 54

Zr2SnC 279 92 97 272 111 155.77 252 104 0.226 48

Zr2SC 326 103 119 351 160 187.22 318 130 0.218 50

Zr2InC 251 62 58 215 73 119.22 204 84 0.214 54

Zr2InN 241 71 89 223 85 133.66 203 81.4 0.246 54

Zr2PbC 219 70 67 206 68 116.88 174 71.4 0.246 54


Fig. 6. Bulk moduli (Bv), shear moduli (Gv) and Young’s moduli (Ev) of 50 Max Phases.

Table 5. Ascending to descending values of bulk modulus (Bv), Young’s modulus (Ev), shear modulus (Gv) and Possion’s ratio of all the MAX phase compounds.

Compounds Bv Compounds Ev Compounds Gv Compounds ν

α-Ta4AlC3 266 β -Ta4AlC3 404 β -Ta4AlC3 162 Ta2GaN 0.292

β -Ta4AlC3 263.11 α-V4AlC3 384 α-V4AlC3 160 Cr2GeC 0.288

V2PC 226.22 V2PC 376 V2PC 154 α-Ta4AlC3 0.272

Ta2GaN 222.66 α-Ta4AlC3 364 Ti4AlN3 153 Ti2CdC 0.249

Nb2PC 218.22 Ti4AlN3 359 Cr2AlC 146 Ti3SiC2 0.248

α-Nb4AlC3 215.77 α-Nb4AlC3 353 α-Nb4AlC3 144 Ti2InN 0.248

α-V4AlC3 212.88 Cr2AlC 351 Ti3GeC2 144 Nb2AsC 0.247

Nb2SnC 210.11 Ti3GeC2 345 Ti4GeC3 143 Hf2SnN 0.247

Nb2AsC 209.22 Ti4GeC3 341 α-Ta4AlC3 143 Ta2GaC 0.247

Hf2SC 204.55 Hf2SC 336 Ta4GaC3 140 V2GaN 0.246

Ti3SiC2 203.88 Nb2PC 333 Hf2SC 137 Nb2GaC 0.246

V2AsC 203.88 Ta4GaC3 332 V2AlC 136 Zr2InN 0.246

Cr2GeC 196.22 V2GaC 326 V2GaC 136 Zr2PbC 0.246

Ta2GaC 193.88 V2AlC 324 Nb2SnC 134 Ti2PbC 0.245

Ta2AlC 193.11 Ti3AlC2 321 Nb2PC 134 Nb2PC 0.245

Cr2AlC 192.88 V2AsC 318 Ti3AlC2 132 β -Ta4AlC3 0.244

Ti3GeC2 191.11 Zr2SC 318 Zr2SC 130 Cr2GaC 0.244

Zr2SC 187.22 Nb2AsC 317 V2AsC 128 Nb2InC 0.241

Ti4GeC3 187 Nb2SnC 314 Ti2SC 127 V2AsC 0.24

Cr2GaC 185.22 Ti2SC 310 Nb2AsC 127 Ta2AlC 0.239

Ti4AlN3 182.88 Ti3SiC2 307 Ti2AlN 126 Nb2SnC 0.237

V2GaC 180.88 Ta2AlC 303 Ti3SnC2 124 Hf2PbC 0.236

Nb2GaC 176.88 Ti3SnC2 300 Ti3SiC2 123 α-Nb4AlC3 0.227

Ti2SC 176 Ti2AlN 300 Ta2AlC 122 Ti2GeC 0.227

Ta4GaC3 175.66 Ta2GaC 294 Ti2GaC 121 Mo2GaC 0.227

V2AlC 174.66 Nb2AlC 285 Ta2GaC 118 Nb2AlC 0.226



Compounds Bv Compounds Ev Compounds Gv Compounds ν

V2GaN 173.88 Ti2GaC 283 Ti2AlC 117 Hf2SC 0.226

Nb2AlC 173.44 Cr2GaC 283 Nb2AlC 116 Zr2SnC 0.226

Ti3SnC2 169.44 Hf2SnC 280 V2GeC 114 Hf2SnC 0.225

Hf2SnC 169.44 V2GeC 277 Cr2GaC 114 V2PC 0.222

Mo2GaC 166.77 Ta2GaN 277 Hf2SnC 114 Ti2SnC 0.218

Ti2AlN 162.55 Ti2AlC 272 Mo2GaC 111 Zr2SC 0.218

Ti3AlC2 161.22 Nb2GaC 270 Nb2GaC 108 Zr2InC 0.214

V2GeC 160.55 V2GaN 263 Ta2GaN 107 V2GeC 0.212

Nb2InC 159.22 Ti2GeC 257 V2GaN 106 Ti2SC 0.209

Ti2GeC 157.66 Mo2GaC 257 Ti2GeC 105 Ti3SnC2 0.205

Zr2SnC 155.77 Zr2SnC 252 Zr2SnC 104 Hf2InC 0.204

Ti2GaC 140.88 Cr2GeC 249 Ti2InC 102 α-V4AlC3 0.199

Hf2SnN 139.11 Nb2InC 247 Nb2InC 99.4 V2GaC 0.199

Ti2InN 138 Ti2InC 241 Hf2InC 98.7 Ti3GeC2 0.198

Ti2AlC 135.33 Hf2InC 238 Cr2GeC 96.7 Cr2AlC 0.197

Ti2SnC 134.44 Ti2SnC 226 Ti2SnC 93 Ti4GeC3 0.195

Hf2InC 134.33 Hf2SnN 211 Hf2SnN 84.5 Ti2AlN 0.192

Zr2InN 133.66 Ti2InN 208 Zr2InC 84 V2AlC 0.19

Ti2InC 128.88 Zr2InC 204 Ti2InN 83.3 Ti2InC 0.186

Hf2PbC 126.44 Zr2InN 203 Zr2InN 81.4 Ta4GaC3 0.185

Ti2PbC 119.22 Hf2PbC 191 Hf2PbC 81 Ti3AlC2 0.178

Zr2InC 119.22 Ti2PbC 182 Ti2PbC 73.2 Ti4AlN3 0.172

Zr2PbC 116.88 Ti2CdC 174 Zr2PbC 71.4 Ti2GaC 0.166

Ti2CdC 115.66 Zr2PbC 174 Ti2CdC 69.6 Ti2AlC 0.164

5. MAX Phase Potential Applications

The MAX phases have been proposed for numerous

applications, some of which are discussed briefly below. The

purpose of this section is mostly to show the rich potential

for applications and the range of industries that the MAX

phases could in principle impact.

5.1. Replacement for Graphite at High Temperatures

Graphite is an important high-temperature material used

extensively in many industries. For example, graphite is used

as connectors, heaters, furnace linings, shields, rigid

insulation, curved heating elements, and fasteners in vacuum

furnaces. Graphite is also the material of choice for the hot

pressing of diamond-cutting tools and other materials, for the

construction industry. In general, some of the MAX phases

such as Ti2AlC have several advantages over graphite such as

better wear and oxidation resistance. The ease by which

Ti2AlC can be machined to high tolerances is also an

important consideration. The high strengths, moduli, and

thermal conductivities of the MAX phases are also positive

attributes. Figure 7 shows examples of MAX phase inserts

that were actually tested in industrial dies and performed

quite well.

(a)(b)

Fig. 7. (a, b) MAX-based insets that were tested in industrial dies at elevated temperatures. (Courtesy of 3-ONE-2, LLC.).


5.2. Heating Elements

Fig. 8. Example of Ti2AlC-based heating element resistively heated to 1450 0C in air (Courtesy of Kanthal).

In the late 1990s, Kanthal Corp. licensed the MAX

technology from Drexel University. Given that one of

Kanthal’s core businesses is heating elements, it was not

surprising that MAX phase heating elements were one of the

first applications targeted by the Swedish company. The

heating element shown in figure 8 was heated up to 1350 0C

and cooled down to room temperature for ≈10 000 cycles

(Sundberg et al., 2004). The resistance of the element was

found to be very stable and the protective oxide that formed

was quite adherent and protective. This heating element is

quite versatile and can be used up to 1400 0C in air, argon,

hydrogen, or vacuum.

5.3. High-Temperature Foil Bearings and Other

Tribological Applications

A project funded by the Office of Navy Research led to the

successful development of MAX based materials for foil

bearings, having low friction and wear from room

temperature to 823 K. Figure 9 shows a Ta2AlC/Ag shaft and

a superalloy foil after testing for 10 000 cycles in a rig. The

shaft was rotated at 50 000 rev min-1

[329]. Honeywell Inc.

was further developing this concept.

(a)(b)

Fig. 9. (a) Ta2AlC/Ag composite cylinder mounted on a shaft after 10000 stop–start cycles in a rig test and (b) picture of superalloy foil after rig testing [74].

5.4. Gas Burner Nozzles

Fig. 10. Pictures of Ti2AlC and steel nozzles used in gas burners. The testing

conditions that heavily corroded the steel nozzles did not appear to affect the

MAX-based one.

Owing to its excellent high-temperature properties and

because it forms a protective alumina layer, Ti2AlC-based

MAX phases can be used in gas burning applications where

traditional metallic alloys show limited service life (See Fig.

10). The same MAX compound can also replace metallic

alloys to increase the burner process temperatures up to 1400 0C. Note that, in contrast to traditional ceramics, joining

problems to existing equipment are easily overcome as MAX

nozzles can be readily threaded and thus can directly replace

metallic nozzles.

5.5. Tooling for Dry Drilling of Concrete

In the early 2000s, 3-ONE-2 (a small company Dr. T. El-

Raghy) and Hilti developed tooling for the dry drilling of

concrete, consisting of diamonds in MAX 312 (Ti3SiC2)

segments, which were then brazed to steel. The performance

of the MAX phase segments was reported to be far superior

to that of current diamond/Co segments (Fig. 11 a,b). With

further improvements in design to overcome the problem of

smearing of concrete powders due to high temperatures and

the inadequate toughness of the segments, this material may

be close to market.



Fig. 11. Pictures of, (a) steel hollow cylinder to which diamond/Ti3SiC2 inserts were brazed, after dry drilling of concrete, (b) same as (a), but where the

diamonds were embedded in a Co matrix; and (c) higher magnification of insert after dry drilling. (Courtesy 3-ONE-2.).

5.6. Glove and Condom Formers and Nonstick Cookware

Ansell Healthcare and Drexel University signed a research

agreement for developing gloves and condom formers to

make latex products. The work resulted in the development

of the slip casting technology for manufacturing large, thin-

walled complex parts (see Fig. 12 a–c) and a patent. In 2007,

a patent was issued (El-Raghy and Lyons, 2007) for the use

of the MAX phases and their coatings as durable, stick and

stain and thermal shock resistant, dishwasher safe, cookware,

cutlery, and other cooking utensils.

Fig. 12. Picture of (a) large, hollow, slip cast Ti3SiC2 glove former; (b) and (c) same as (a), but showing thin walls possible; and (d) complex solid and hollow

slip cast parts starting with Maxthal powders. (Courtesy 3-ONE-2.).

5.7. Application in the Nuclear Industry

There are some of the MAX phases compounds, most

notably Ti3AlC2 and Ti3SiC2, are quite resistant to radiation

damage (Le Flem et al., 2010; Liu et al., 2010; Napp´e et al.,

2009; Whittle et al., 2010). There is also a growing body of

evidence that dynamic recovery may be occurring at

temperatures of 700 0C or lower. In a post-Fukushima world,

it is imperative to build some accident tolerance to the

Zircaloy tubes that hold the nuclear fuel. The simplest is to

spray a thin coating of Ti2AlC or Ti3AlC2 onto the Zircaloy

tubes. If the coatings are thin enough and are designed in

such a way that in the presence of oxygen they form a thin

cohesive and adhesive alumina layer, then it is possible to

protect the Zircaloy tubes in the case of accident due to loss

of coolant. The challenge, however, is to thermally spray the

Ti2AlC such that it does not lose its ability to form thin

alumina layers. The current text on the topic shows that after

high-velocity oxy-fuel, HVOF, spraying of Ti2AlC, heating in

air results in the formation of titania instead of alumina

(Frodelius et al., 2008; Sonestedt et al., 2010a,b). The fact


that Ti3SiC2 does not react with molten Pb and or Pb–Bi

alloys (Barnes, Dietz Rago, and Leibowitz, 2008; Heinzel,

M¨uller, and Weisenburger, 2009; Utili et al., 2011) renders it

a good material to be used for containing molten Pb or Pb–Bi

alloys in nuclear reactors. In a recent paper, Sienicki et al.

(2011) suggested that Ti3SiC2 could be used in an improved

natural circulation Pb-cooled small modular fast reactor.

5.8. Ignition Devices and Electrical Contacts

Some of the MAX phases are used as the conductive

element in spark plugs and other such ignition devices

(Walker, 2010).One of the first applications for Ti3SiC2 was

by a small Swedish company, Impact Coatings, as sputtering

targets for the deposition of electrical contacts. Although the

company now uses other cheaper targets, this early

application is significant. Currently, others are sputter

depositing Cr2AlC thin films on steels and turbineblades (e.g.

Hajas et al., 2011). In some cases, MAX phase targets are

used. On the basis of the growing worldwide interest in the

MAX phases, it is reasonable to assume that a market for

sputter targets should emerge soon. Owing to their good

electrical conductivity and tribological properties, in addition

to the acceptable mechanical properties, MAX phases such as

Ti3SiC2 and Ti3AlC2 have been shown to perform better than

carbon based pantographs for electric trains. Currently, a few

leading projects are running in China, aiming for application

on the high speed railway under construction.

5.9. Electrical Contact for SiC-based Devices

Presently, SiC-based devices are under development for

use in electronic devicesthat are subjected to high

temperatures and/or corrosive environments. Siliconcarbide’s

material properties (large band-gap, high-thermal

conductivity, extremely high-melting and decomposition

temperatures, excellent mechanical properties, and

exceptional chemical stability) are far superior to those of Si

and render it suitable for operation in hostile environments.

Because its band gap is nearly three times larger than that of

Si, it is possible to use SiC as a semiconductor, for example,

to temperatures as high as 1000 0C because of its low

intrinsic carrier concentrations and operation within the

dopant-controlled saturation regime required for

semiconducting devices. One of the challenges of this

technology isto find a material to use as an electrical contact

that does not react with SiC at elevated temperatures and

results in low contact resistances. In 2003, a patent was

issued (Tuller, Spears, and Mlcak, 2003) for the use of

Ti3SiC2 as an electrical contact for SiC electronic

components. The major advantage of Ti3SiC2 is that it is in

thermodynamic equilibrium with SiC. This would in turn

allow the SiC devices to be operated in high-temperature

environments without the contact material reacting with the

SiC, and deteriorating the performance of the device. Some

sensor applications are based on SiC field effect transistors

that exploit the wide band gap of SiC and its chemical

inertness. In such applications, there is also need a

compatible inert electrode material such as Ti3SiC2.

5.10. Forming Processes and Sintering

One of the crucial advantages of working with the MAX

phases is that they can be pressureless sintered to full density

by heating green performs in inert atmospheres such as argon.

The first report in the open literature for the pressureless

sintering of a MAX phase to full density can be found in a

patent that issued in 2002 (El-Raghy et al., 2002). The first

paper published in 2004 (Murugaiah et al., 2004) not only on

the pressureless sintering of Ti3SiC2 but also on its tape

casting, a process that, not surprisingly, led to orienting the

flaky prereacted hexagonal grains. In this paper, it was shown

that the simplest method to producing highly oriented

microstructures was to gently shake or tap the dies containing

the prereacted Kanthal powders prior to sintering. The first

paper published on the pressureless sintering in 2006 (Zhou

et al., 2006). In general, the fact that the MAX phases can be

sintered to full density, without the application of pressure is

an important attribute that greatly enhances their chances for

commercialization. The methods for forming the green

bodies are quite varied. They range from slip casting, to

produce complex, thin wall shapes (e.g., Figure 11),

extrusion to form tubes (Figure 9), cold pressing to form

simple shapes (Figure 7) and cold isostatic pressing to metal

injection molding. It is significance noting that the inherent

ductility of the MAX phases help to forming green bodies

without help of any binder. Spark plasma sintering (SPS) is

also emerging as a viable method to fabricate and densify the

MAX phases (Cui et al., 2012; Hu et al., 2009, 2011b; Zhang

et al., 2003). Currently there is little work, however,

comparing the high-temperature properties of samples made

by SPS with those made by reactive hot pressing or

pressureless sintered commercial powders.

In addition to the applications mentioned above, a number

of other potential applications have been found. These

include: electrodes, exhaust gas filters for automobiles, free-

cutting elements, microelectronics, biomaterials, damping

materials (high stiffness and up to high temperatures),

corrosion resistant materials, surface coatings, defense

applications, such as armor, nuclear applications, low

dimensional materials, and substrates for CVD diamond.

6. Conclusion

The MAX phases have attracted considerable attention and

are garnering new devotees because they have a quite

unusual combination of properties. The fact that their

chemistries can be altered while keeping the structure the

same allows for relatively rapid understanding. The

emergence of possibly magnetic MAX phases is an exciting

development that would greatly enhance their potential

applications. On the mechanical side, the fact that

dislocations are confined to 2D is proving invaluable in

elucidating the deformation behavior of layered solids in

general, and ones that are also conductive in particular. The

most urgent issue in MAX phase research is to develop



viable commercial applications for these materials. With the

preliminary and potential application fields discussed above,

market penetration by MAX phase materials will create more

stimuli to carry out more research and development on this

family of layered metallic ceramics. Research on MAX

phases is currently funded by agencies, science foundations

and defense industries in the USA, China, Europe and

Australia. However, funding for research on MAX phases

from governmental agencies in Japan is almost zero. The

likelihood of the Japanese government funding such research

remains small until a clear market scenario is available.

Another important issue is the search for new MAX phases.

First, to better understand the MAX phases themselves, both

those known to exist and those theoretically predicted to be

thermodynamically and mechanically stable. To do so,

thorough experimental investigations into the properties are

needed. The second priority is to discover more MAX phases.

It is encouraging that in the past few years many MAX

phases, particularly 413 and 312 phases, have been

discovered. More 312 or 211 MAX phases, plus their solid

solutions, which are numerous, are awaiting exploration. In

this review paper we have studied most of the MAX phase

compounds, their different properties and applications in

different sectors. We hope that the researches described in

this overview will be helpful for the discovery of new MAX

phase compound and their practical and possible applications

in modern technology in near future.

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Study on Structural, Electronic, Optical and Mechanical ...article.ajmp.org/pdf/10.11648.j.ajmp.20150402.15.pdf · Md. Atikur Rahman *, Md. Zahidur Rahaman Department of Physics,